Huh? The cotton gin didn't pick the cotton. The cotton gin separates the seeds and their hull from the fibers. Slaves still picked cotton 60-70 years after the invention of the cotton gin.
It was soft and smooth going down, but kinda' got stuck in my throat.
Also, it doesn't really mix well with tonic water.
The point is machines would be invented to do much of the work Illegal Immigrants do if it was necessary. (And farmers would invest in these machines and use them if they didn't have Illegal Immigrants to exploit.)
For example: Many trees are now shaken to release the friut instead of having people pick each fruit from the tree.
Being the product of a long line of farmers I can concur that the lack of human labor has always boosted the invention and use of machines to do the work.
Many Central Valley producers have not mechanized because cheep labor was available.
You are right about the cotton gin but mechanical harvesters did come along when finally the labor dried up or became too expensive.